R+7=-6+5r+8-3r
Please write this as a word problem

There are basically 6 ratios used for finding the elements in Trigonometry. They are called trigonometric functions. The six trigonometric functions are sine, cosine, secant, cosecant, tangent and cotangent.

By using a right-angled triangle as a reference, the trigonometric functions and identities are derived:

sin Î= Opposite Side/Hypotenuse

cos Î= Adjacent Side/Hypotenuse

tan Î= Opposite Side/Adjacent Side

sec Î= Hypotenuse/Adjacent Side

cosec Î= Hypotenuse/Opposite Side

cot Î= Adjacent Side/Opposite Side

All these are taken from a right-angled triangle.

When the height and base side of the right triangle are known, we can find out the sine, cosine, tangent, secant, cosecant, and cotangent values using trigonometric formulas.

The reciprocal trigonometric identities are also derived by using the trigonometric functions.

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Answer: The linear function is represented by f(x) = (4x/3) + 12

Step-by-step explanation: Taking a linear function's equation pattern to be the graph of y = ax + b, plot the sollutions for such:

(8) = (-3)a + b, and similarly: (-4) = 6a + b, solving for that will lead to a = (4/3) and b = (12), thus: f(x) = (4x/3) + 12.

The function value is 5/2 when x is 0 and value of function is 4 when x =-3.

A relation is a function if it has only One y-value for each x-value.

The given function is f(x)=|1-x|/2 + 2

We need to find the value of function when x is 0 and when x is -3.

Plug in value x =0

f(0)=|1-0|/2+2

=1/2+2

f(0)=5/2

Now we have to find the function when x is -3

f(-3)=|1+3|/2+2

=4

Hence, the function value is 5/2 when x is 0 and value of function is 4 when x =-3.

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If x is not equal to -2 or -6, an expression that is comparable to the rational expression exists.

Math allows for addition, subtraction, multiplication, and division. Following is the structure of an expression: Calculator, number or variable, and expression The components of a mathematical expression include numbers, variables, and operations (such as addition, subtraction, multiplication or division etc.) You can contrast phrases and expressions.

given

Both the numerator and the denominator share the value x + 2, however there is a gap at x + 2 = 0, which also exists at x = -2.

Furthermore, if the denominator is zero, a function is undefined.

At x = -6, the denominator is zero as well.

Therefore, the function is undefined at x = -6, or there is a vertical asymptote at x = -6 and a hole at x = -2.

If x is not equal to -2 or -6, an expression that is comparable to the rational expression exists.

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Since the variables or exponent raised to these variables are "unlike" or different, these terms are referred to as unlike terms.

A variable is, to put it simply, a quantity that may be altered and is not fixed. The two primary categories of variables are categorical and numeric. Then, for categorical and numerical variables, respectively, nominal or ordinal and discrete or continuous subcategories are created for each category. This section provides a quick overview of these types. a quantity that could take any of a range of values. a variable's sign; something that is variable; a component of a scientific experiment that is potentially subject to change.

given

Like terms are those terms that share the same factors.

Consequently, phrases that have identical variables raised to the same exponent are considered similar terms.

What are 25, -3x, and 3x called then , Since the variables or exponent raised to these variables are "unlike" or different, these terms are referred to as unlike terms.

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Answer:

6 1/2

Step-by-step explanation:

1 1/6+ 2 1/6+ 3 1/6=6 3/6

Then you would simplify and get 6 1/2

A two-variable equation having a graph in the form of a line is referred to as linear.

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

A two-variable equation with a line-shaped graph is said to be linear. The set of points in the coordinate plane that make up the graph of the linear equation are all the solutions to the problem.

Given, 2x - 3y = 7

(k + 1)x + (1 - 2k)y = 5k - 4

Here [tex]$a_1=2, b_1=-3, c_1=7$[/tex]

[tex]$$\mathrm{a}_2=\mathrm{k}+1, \mathrm{~b}_2=1-2 \mathrm{k}, \mathrm{c}_3=5 \mathrm{k}-4$$[/tex]

Since equations (1) and (2) have infinite solutions

[tex]$& \frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_3} \\[/tex]

substitute the values in the above equation, we get

[tex]$& \Rightarrow \frac{2}{\mathrm{k}+1}=\frac{-3}{1-2 \mathrm{k}}=\frac{7}{5 \mathrm{k}-4} \\[/tex]

simplifying the equation, we get

[tex]$& \therefore \frac{2}{\mathrm{k}+1}=\frac{3}{1-2 \mathrm{k}} \\[/tex]

[tex]& \Rightarrow 2(1-2 \mathrm{k})=-3(\mathrm{k}+1) \\[/tex]

[tex]& \Rightarrow 2-4 \mathrm{k}=-3 \mathrm{k}-3 \\[/tex]

[tex]& \Rightarrow 2+3=-3 \mathrm{k}+4 \mathrm{k} \\[/tex]

Therefore, the value of K = 5.

The complete question is:

What value of K will be following pair of linear equations have infinite solutions

[tex]$$\begin{aligned}& 2 \mathrm{x}-3 \mathrm{y}=7 \\& (\mathrm{~K}+1) \mathrm{x}+(1-2 \mathrm{~K}) \mathrm{y}=(5 \mathrm{~K}-4)\end{aligned}$$[/tex]

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Answer:

32=3x-7

Step-by-step explanation:

Step-by-step explanation:

a. The profit function, P(x), can be found by subtracting the cost function from the revenue function.

P(x) = R(x) - C(x)

P(x) = (-0.04x² + 320x) - (85x + 120,000)

P(x) = -0.04x² + 235x - 120,000

b. To find the profit if 1000 bicycles are produced and sold, substitute x=1000 into the profit function:

P(1000) = -0.04(1000)² + 235(1000) - 120,000

P(1000) = -40,000 + 235,000 - 120,000

P(1000) = 75,000

So, the profit would be $75,000 if 1000 bicycles are produced and sold.

c. To find the break-even point, we set the profit function equal to zero and solve for x:

P(x) = 0

-0.04x² + 235x - 120,000 = 0

Using the quadratic formula or factoring, we can find that the break-even point occurs when:

x = (235 +/- sqrt(235^2 - 4(-0.04)(-120,000)))/(2(-0.04))

x = (235 +/- sqrt(55,089,000))/(-0.08)

x = (235 +/- 7,500)/(-0.08)

x = (235 - 7,500)/(-0.08) or (235 + 7,500)/(-0.08)

x = -31,250/ -0.08 or 5,375/-0.08

x = 3906.25 or -64,375

Since negative values of x do not make sense in this context, the break-even point occurs when 3906.25 bicycles are produced and sold.

A system of equations that has no solution can be represented by two lines in a coordinate plane that are parallel.

A system of equations is said to have no solution if there is no set of values that can simultaneously satisfy both equations. This can occur when the equations are inconsistent, meaning that they cannot be true at the same time, or when the equations are dependent, meaning that one equation is a multiple of the other.

Parallel lines have the same slope but different y-intercept, this means that there's no point that belongs to both lines, that's why the system has no solution.

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So, the probability that a customer buys either pet supplies or baby supplies is 0.77.

The probability that a customer buys either pet supplies or baby supplies is represented by P(A U B).

Using the formula for the probability of the union of two events: P(A U B) = P(A) + P(B) - P(A ∩ B),

We can substitute in the given probabilities: P(A U B) = 0.64 + 0.25 - 0.12

Therefore, the equation that represents the probability that a customer buys either pet supplies or baby supplies is:

P(A U B) = 0.64 + 0.25 - 0.12 = 0.77

This means that the probability that a customer buys either pet supplies or baby supplies is 0.77.

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For the three red lights, we have a "9 sockets choose 3" option. In those 9C3 methods. The solution is 1260 (9C3) (6C4)(2C2).

For the three red lights, we have a "9 sockets choose 3" option. In those 9C3 methods.

There are now just 6 open sockets after the 3 red bulbs have been installed.

Put three red bulbs in the first three sockets.

None = 9C3

There are 4 yellow bulbs in 4 sockets.

Way count is 6C4

Two sockets hold two blue bulbs.

Number of ways = 2C2

For the four yellow lights, we have a choice of "6 sockets, choose 4" 6C4 in that manner.

There are just 2 open sockets left once the 4 red lights are screwed in.

The blue lights are available in "2 sockets pick 2." Consequently, (2C2) = 1 way.

Once those two bulbs were screwed in, a bulb was present in each socket.

Total number of methods is 84 * 15 * 1 or 9C3 * 6C4 * 2C2.

1260 different ways in total.

So, there are 1260 total ways.

The solution is 1260 (9C3) (6C4)(2C2).

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The value of x is 2.045 by simple algebra.

Use the time formula, t = d/s, which states that time is equal to distance divided by speed, to solve for time. Time is a function of both speed and distance.

Until it reaches its destination 200 miles distant, a car is driving on a little highway at either 55 or 35 miles per hour, depending on the posted speed restrictions.

x is the duration, in hours, that the vehicle is travelling at 55 mph.

Y is the duration, in hours, that the vehicle is travelling at 35 mph.

55x + 35y = 200 is the equation defining the relationship.

We must locate:

If the trip takes the car 2.5 hours at 35 miles per hour, how long does it take to travel at 55 miles per hour?

∵ 55x + 35y = 200

The drive takes the car 2.5 hours at a speed of 35 mph.

Y shows the duration of time for an automobile travelling at 35 mph.

∴ y = 2.5

- To obtain the value of x, substitute the value of y into the equation.

∴ 55x + 35(2.5) = 200

∴ 55x + 87.5 = 200

- Take 87.5 off of both sides.

∴ 55x = 112.5

- Subtract 55 from both sides.

x equals 2.045 hours.

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The graph that matches the inequality equation represented as 3x − 2y ≥  4 is

A. The graph shows a solid line, which crosses the y-axis at negative 2 and the x-axis at 4 thirds, with shading above the line.

There are some points that help in interpreting inequality graphs.

The first part is to arrange the equation in the form so that y is the subject of the formula and to the left.

3x − 2y ≥  4

-2y ≥ 4 - 3x

y ≤ 3/2 x - 2

Then watch out for dashed lines or solid lines

dashed lines means there is no equality sign in the inequality > OR <

solid line means there is equality in the inequality  ≤ OR ≥

Another part is the shaded portion

shading above the line defines greater than

shading below the line defines less than

comparing with y = mx + b shows that the intercept which is b is -2

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To graph the system of inequalities:

y ≤ −5x + 2

y < 3x − 1.5

We can start by graphing the boundary lines for each inequality:

For y ≤ −5x + 2, the boundary line is y = -5x + 2, which has a slope of -5 and a y-intercept of 2. Since the inequality includes "less than or equal to," we will use a solid line to represent the boundary.

For y < 3x − 1.5, the boundary line is y = 3x - 1.5, which has a slope of 3 and a y-intercept of -1.5. Since the inequality is "less than" and not "less than or equal to," we will use a dashed line to represent the boundary.

Next, we need to determine the shading for each inequality:

For y ≤ −5x + 2, we shade below the solid line because y is less than or equal to the other side of the inequality.

For y < 3x − 1.5, we shade below the dashed line because y is less than the other side of the inequality.

Based on the given options, the correct answer is:

The graph shows a solid line that passes through 0 comma 2 and 1 comma negative 3, with shading below the line. There is also a dashed line that passes through 0 comma negative 1.5 and 1 comma 1.5, with shading below the line.

In this exponential growth function, after 5 hours it contains 1944mg and after 6 hours it contains 5832mg.

What is exponential function?

An exponential function is defined by the formula f(x) = aˣ, where the  x is any real number , acts as an exponent. The exponential curve depends on the exponential function  which  depends on the value of the x.

Where a>0 and a is not equal to 1.

If many functions, “x” is a variable and “a” is a constant, which is the base of the function.

Given that, every hour, the mass of bacteria in a sample multiplies by 3.

Then the exponential function can be taken as f(x)= 3ⁿ x where f(x)= mass of bacteria, n=time(hours), x= original mass.

Here x= 8 mg

a) if n=5 hours then the exponential function will be

f(x)= 3⁵ × x

putting x=8 we get,

f(8)= 3⁵ × 8

 = 1944

b) if n=6 hours then the exponential function will be

f(x)= 3⁶ × x

putting x=8 we get,

f(8)= 3⁶ × 8

 = 5832

Hence, after 5 hours it contains 1944mg and after 6 hours it contains 5832mg.

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The mean absolute deviation of Restaurant B's service ratings is equal to 1.0567111111111.

Mathematically, the mean for this set of service ratings can be calculated by using the following formula:

Mean = [F(x)]/n

For the total number of service ratings, we have;

F(x) = 4 + 4 + 2 + 1 + 4 + 4 + 2 + 3 + 5 + 1 + 5 + 3 + 2 + 2 + 2 + 3 + 1 + 2 + 2 + 4 + 2 + 2 + 3 + 2 + 2 + 3 + 2 + 4 + 5 + 3 + 3 + 2 + 5 + 3 + 5 + 1 + 3 + 1 + 3 + 1 + 2 + 4 + 3 + 3 + 2 + 4 + 4 + 1 + 3 + 5 + 1 + 3 + 3 + 4 + 5 + 4 + 2 + 3 + 5 + 2 + 4 + 3 + 2 + 4 + 4 + 4 + 1 + 2 + 5 + 5 + 5 + 3 + 5 + 4 + 1

F(x) = 226.

Note: The total number of data (n) is equal to 75.

Next, we would determine the mean ratings as follows;

Mean = [F(x)]/n

Mean ratings = 226/75

Mean ratings = 3.0133333333333.

In Mathematics, MAD is an abbreviation for mean absolute deviation and the mean absolute deviation (MAD) of a data set can be calculated by using this formula;

MAD = 1/n ∑|x - μ|

Where:

Substituting the given parameters into the MAD formula, we have the following;

MAD = 1/75 [(4 - 3.0133333333333) + (4 - 3.0133333333333) + (2 - 3.0133333333333) + (1 - 3.0133333333333) + ........ + (1 - 3.0133333333333)]

MAD = 1/75 × 79.25333333325.

MAD = 1.0567111111111.

In conclusion, the mean absolute deviation (MAD) for Restaurant B's service ratings is 1.0567111111111.

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Answer:

definatly fan, i do not know about the water heater if it blows air then i think its true  last 2 i would select

Step-by-step explanation:

Answer:

it's a fan cause a turbine is currently a fan

The expanded form of the expression is  1/2 x - 1/2 y which is determined by the distributive property.

Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.

The expression is given in the question, as follows:

-1/2 (y - x)

We have to determine the expanded form of the expression.

As per the question, we have

⇒ -1/2 (y - x)

Apply the distributive property of the multiplication,

⇒ -1/2 × y - (-1/2) × x)

⇒ -1/2 y + 1/2 x

⇒ 1/2 x - 1/2 y

Hence, the expanded form of the expression is 1/2 x - 1/2 y.

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Answer:-2, 4

Step-by-step explanation:

The height of the line in a frequency polygon and the height of the bars in a histogram both represent the frequency or count of the data in a particular category or range of values.

What is Polygon?

In two dimensions, a polygon is a closed object made up of segments of straight lines that join at least three points. A polygon in mathematics can be convex or concave and have any number of sides.

The height of the line in a frequency polygon is proportional to the frequency of the data. The frequency value is marked at the highest point of the line, which is drawn between the midpoints of each category or range of values.

The height of the bar in a histogram, which is proportional to the number of data points in that category or range of values, denotes the frequency of the data. To depict the frequency distribution of the data, bars are drawn next to one another with no space in between.

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The height of the line in a frequency polygon and the height of the bars in a histogram both represent the frequency or count of the data in a particular category or range of values.

What is Polygon?

In two dimensions, a polygon is a closed object made up of segments of straight lines that join at least three points. A polygon in mathematics can be convex or concave and have any number of sides.

The height of the line in a frequency polygon is proportional to the frequency of the data. The frequency value is marked at the highest point of the line, which is drawn between the midpoints of each category or range of values.

The height of the bar in a histogram, which is proportional to the number of data points in that category or range of values, denotes the frequency of the data. To depict the frequency distribution of the data, bars are drawn next to one another with no space in between.

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An algebraic expression that contains one or more monomials.

A polynomial factor P(x) is any polynomial that divides evenly into P. (x). x + 2 is, for example, a factor of the polynomial x2 – 4. A polynomial’s factorization is its representation as a product of its components. For example, (x – 2)(x + 2) is the factorization of x2 – 4.

Step 1: Group the first two terms together, followed by the last two terms. Step 2: Extract a GCF from each binomial separately. Step 3: Remove the common binomial. It is worth noting that if we multiply our answer by itself, we get the original polynomial. Polynomial. An algebraic expression containing one or more monomials. Monomial. A number, a variable, or a number-variable product

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The scale factor is 1/2.

What is a scale factor?

When both the original dimensions and the new dimensions are known, the scale factor may be determined. The following is a basic formula to determine a figure's scale factor: Scale factor is equal to the difference between the dimensions of the old and new shapes.

Here, we have

Given: ΔDEF is a dilation image of ΔABC.

Let

z is the scale factor

z = DE/AB

We have

DE = 4units

AB = 8units

z = 4/8

z = 1/2

Hence, the scale factor is 1/2.

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Answer:

y = 163°

Step-by-step explanation:

Vertically opposite angles are equal. So, y = 163°

Also, the points u give for the question is halved for the person who writes the answer. So, I will get 10 points, not 20. Anyways, Cheers!

The proof of the area of the circle equation is shown below

From the question, we have the following parameters that can be used in our computation:

Area of radius 1 = π

The area of a circle is proportional to the square of its radius.

When the radius is multiplied by a scale factor of "r," the area is multiplied by the square of that factor: r^2.

So, the area of a circle of radius "r" is given by π * r^2 square units.

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Text messages costing $0.05/text will have an expression C = 0.05t for cost of t amount of text messages.

What is an expression?

A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation.

The cost of 1 text message is = $0.05

Let the number of text messages be t.

The cost (C) for t number of text message will be -

C = t × 0.05

C = 0.05t

Therefore, the expression is C = 0.05t.

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The required symbol of logarithmic function is [tex]\log_{e}x[/tex].

A logarithmic equation is one that uses the logarithm of an expression involving a variable. Check to verify if you can write both sides of the equation as powers of the same number before attempting to solve an exponential equation.

The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b. For instance, because 1000 is equal to 103, its logarithm in base 10 is 3, or log10 (1000) = 3. When there is no possibility of mistake or when the base is irrelevant, The logarithm of x to base b is expressed as logb (x), logb x, or even without the specified base, log x, just like in big O notation.

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Carlos has 28 pennies, 28 dimes, and 20 quarters.

Value is a concept that is used to describe the worth or importance of something or someone. It is often related to an individual's beliefs and opinions and is used to measure the quality of an item or service. Value is a subjective concept, as what is considered valuable to one person may not be valuable to another. Value can also be measured in terms of money, with items or services valued at a certain price.

The total value of the coins is $6.59. Each penny is worth 1 cent, each dime is worth 10 cents, and each quarter is worth 25 cents. Therefore, 28 pennies plus 280 dimes (28 x 10) plus 500 quarters (20 x 25) equals 858 cents, which is equal to $6.59.

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In the given cube-shaped cake, the value of c + s = 32/5.

In the given figure of the cube-shaped cake, let [RNQ] be the area of the triangle RNQ. The volume of the corresponding piece c = 2[RNQ]. The cake piece has icing on the top and on the vertical side that contains the edge QR. Hence the total area with icing is [RNQ] + 2^2 = [RNQ] + 4. Hence, c+s = 3[RNQ] + 4.

In order to determine [RNQ], introduce a coordinate system. Let Q be the origin. As the length of each edge is 2. Hence,

Q = (0,0)

P = (2, 0)

R = (0, 2)

In the coordinate system, as M is the midpoint of PS, M = (2, 1). The equation of the line QM is:

m = (1- 0)/(2 – 0) = ½

y – 0 = ½(x – 0)

2y – x = 0

As the line RN is orthogonal to QM, it has an equation is y + 2x + q = 0. As the point R lies on the line RN,

2 + 2(0) + q = 0

q = -2

Hence, RN is y + 2x -2 = 0

Substituting x = 2y into the line RN,

y + 2(2y) -2 = 0

5y = 2

y = 2/5

x = 2(2/5) = 4/5

In the triangle RNQ, x is the height from N onto RQ, the area [RNQ] = (x*RQ)/2 = 2x/2 = x = 4/5.

Hence, 3[RNQ] + 4 = 3(4/5) + 4 = 32/5.

Note: The question is incomplete. The complete question probably is: A cubical cake with edge length 2 inches is iced on the sides and the top. It is cut vertically into three pieces as shown in this top view, where M is the midpoint of a top edge. The piece whose top is triangle B contains c cubic inches of cake and s square inches of icing. What is c+s?

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The answer to the question is 17/140 fraction.

A fraction is a numerical expression that represents a part of a whole or a ratio of two numbers. It consists of two parts: a numerator (the number on top) and a denominator (the number on the bottom). For example, 3/4 is a fraction that represents 3 parts out of 4. It can also represent the ratio of 3 to 4.

To move the fraction to each box, you would need to multiply the denominator of the first fraction (10) by the numerator of the second fraction (14). The result is 140. Then, you would add the numerator of the first fraction (3) to the numerator of the second fraction (14), giving you 17. The answer to the question is 17/140.

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